SOLVED PAPER 2024 (CDS) (I) (Mathematics)

Total Questions: 100

1. Find the value of this -

Correct Answer: (a)
Solution:

2. The speeds of four cars are 2u, 3u, 4u and xu and the time taken by them to cover the same distance is xt, 4t, 3t and 2t respectively, where x, u, t are real numbers. What is the value of x?

Correct Answer: (b) 6
Solution:Distance = Speed × Time
According to question,
2u × (xt) = 3u × 4t
⇒ 2x = 12
∴ x = 12/2 = 6
Hence, value of x will be 6.

3. If m : n = 1 : 2 and p : q = 3 : 4, then what is (2m + 4p) : (n + 3q) equal to?

Correct Answer: (a) 1 : 1
Solution:

4. If the rate of interest is 5%, then what would be the difference between compound interest and simple interest received on 10, 000 (each) after 3 yr from now?

Correct Answer: (c) 76.25
Solution:

5. A person bought a book at 3/4ᵗʰ of its listed price and sold it at 50% more than its listed price. What is the percentage of gain in the transaction?

Correct Answer: (d) 100%
Solution:

6. If the difference between the interior and exterior angles of a regular polygon is 144°, then what is the number of sides of the polygon?

Correct Answer: (d) 20
Solution:Let, the internal and external angle of regular polygon is a and b, respectively.

So, a + b = 180° ......(i)
a - b = 144° ......(ii)
Adding Equations. (i) and (ii),
We have, 2a = 324°
∴ a = 162°
Put the value of a in Eq. (i),
b = 180° - 162° = 18°
We know,
Internal angle of polygon having 'n' sides
⇒ ((n - 2) × 180°)/n
⇒ 162° = ((n - 2) × 180°)/n
⇒ 162n = 180n - 360°
⇒ 18n = 360°
∴ n = 20
Hence, number of sides of polygon = 20

7. If the sum and product of the roots of a quadratic equation are 2 and - 100 respectively, then which of the following is correct?

Correct Answer: (c) The is only one such equation which is x² - 2x - 100 = 0
Solution:Let the roots of the required equation be α and β.

Then, alpha + beta = 2 and alpha*beta = - 100
Required equation is
x² - (α + β)x + α β = 0
⇒ x² - (2)x + (-100) = 0
⇒ x² - 2x - 100 = 0
Hence, there is only one such equation.

8. If 2 is a zero of the polynomial p(x) = x³ + 3x² - 6x - a then what is the sum of the squares of the other zero's of the polynomial?

Correct Answer: (b) 17
Solution:

9. If t = cos 79° then what is cosec 79° (1 - cos 79°) equal to?

Correct Answer: (d)
Solution:

10. Find the value of this -

Correct Answer: (b) λ - δ
Solution: